Solutions of the Differential Inequality with a~Null Lagrangian: Regularity and Removability of Singularities

Abstract

We prove a theorem on self-improving regularity for derivatives of solutions of the inequality $F(v^{\prime }(x))\le KG(v^{\prime }(x))$ constructed by means of a quasiconvex function $F$ and a null Lagrangian $G$. We apply this theorem to improve the stability and Hölder regularity results of \cite{Egor2008} and to establish a theorem on removability of singularities for solutions of this inequality.